The Dimension-Shift Category and Its Mellin-Gamma Representation

Fuente: arXiv

Enregistré dans:

Détails bibliographiques
Auteur principal:	Santacana, Andreu Ballus
Format:	Preprint
Publié:	2025
Sujets:	Representation Theory Classical Analysis and ODEs Category Theory 18M05, 28A33, 43A05, 33B15
Accès en ligne:	Acceder al recurso
Tags:	Ajouter un tag Pas de tags, Soyez le premier à ajouter un tag!

Documents similaires

Radial Integration in Continuous Dimension: A Mellin-Gamma Classification of Euclidean Ball Volume
par: Santacana, Andreu Ballus
Publié: (2026)

$a$-potent Schwarz matrices and Bessel-like Jacobi polynomials
par: Dyachenko, Alexander, et autres
Publié: (2024)

Commutativity and Kleisli laws of codensity monads of probability measures
par: Shirazi, Zev
Publié: (2024)

Some new properties of the beta function and Ramanujan R-function
par: Yang, Zhen-Hang, et autres
Publié: (2024)

Hyperelliptic values of the Gamma function
par: Lügering, Jan
Publié: (2021)

A bibasic double sum extension of a $q$-binomial theorem arising out of subspace enumeration
par: Bhatnagar, Gaurav, et autres
Publié: (2026)

Fourier Analysis via Mild Distributions: Group Theoretical Aspects
par: Feichtinger, Hans G
Publié: (2024)

Symmetries of coefficients of three-term relations for basic hypergeometric series
par: Yamaguchi, Yuka
Publié: (2025)

Hyperdeterminantal Total Positivity
par: Johnson, Kenneth W., et autres
Publié: (2024)

The $q$ and $q^{-1}$-symmetric orthogonal polynomials in the $q$-Askey scheme, their dual polynomials and functions, orthogonality, generating functions and relations and nonterminating $q$-Chaundy double product representations
par: Cohl, Howard S., et autres
Publié: (2023)

On the Dotsenko-Fateev complex twin of the Selberg integral and its extensions
par: Neretin, Yury A.
Publié: (2022)

Weierstrass functions and a generalization of the additive-multiplicative Weierstrass inequality
par: Wiśniewska, Halina
Publié: (2025)

On the incomplete Lauricella matrix functions of several variables
par: Verma, Ashish
Publié: (2020)

A new index transform with the square of Whittaker's function
par: Yakubovich, Semyon
Publié: (2025)

Generalized product formulas for Whittaker's functions and a novel class of index transforms
par: Yakubovich, Semyon
Publié: (2025)

Bilateral discrete and continuous orthogonality relations in the $q^{-1}$-symmetric Askey scheme
par: Cohl, Howard S., et autres
Publié: (2024)

Recurrence relations for the coefficients of the confluent and Gauss hypergeometric functions in the complex plane
par: Xu, Zi-Qiao, et autres
Publié: (2026)

Sewing lemma and knitting lemma for metric spaces
par: Curry, Charles H. A., et autres
Publié: (2025)

Combinatorics of generalized orthogonal polynomials of type $R_{II}$
par: Kim, Jang Soo, et autres
Publié: (2024)

Mapping properties of the $S$-operator
par: Kang, Hunseok, et autres
Publié: (2026)

Abel's problem, Gauss and Cartier congruences over number fields
par: Delaygue, Éric, et autres
Publié: (2025)

On the Use of the Mellin Transform to Generate Families of Power, Hyperpower, Lambert and Dirichlet Type Series and Some Consequences
par: Glasser, Larry, et autres
Publié: (2023)

Fourier transform pairs and Eisenstein-type series related to Jacobi elliptic functions
par: Hang, Peng-Cheng, et autres
Publié: (2025)

Connections between $\mathcal{S}$-operators and restriction estimates for spheres over finite fields
par: Kang, Hunseok, et autres
Publié: (2025)

$q$-rious unimodality
par: Warnaar, S. Ole, et autres
Publié: (2025)

Expressing the difference of two Hurwitz zeta functions by a linear combination of the Gauss hypergeometric functions
par: Qi, Feng
Publié: (2025)

Derivatives of Humbert confluent hypergeometric functions with respect to their parameters
par: Shehata, Ayman, et autres
Publié: (2021)

Analytic Dilogarithm Identities
par: Hakimoglu-Brown, Cetin
Publié: (2025)

Rankin--Cohen brackets in Representation Theory
par: Kobayashi, Toshiyuki, et autres
Publié: (2026)

Necessary and Sufficient Conditions for Absolute Monotonicity of Functions Related to Gaussian Hypergeometric Functions
par: Zhao, Tiehong
Publié: (2025)

Unimodality preservation by ratios of functional series and integral transforms
par: Karp, Dmitrii, et autres
Publié: (2024)

Turán's inequality, nonnegative linearization and amenability properties for associated symmetric Pollaczek polynomials
par: Kahler, Stefan
Publié: (2018)

On some Analytic Inequalities for Gauss Hypergeometric Functions via Gruss Discrete Inequality
par: Raissouli, Mustapha, et autres
Publié: (2024)

Two closed-form evaluations for the generalized hypergeometric function ${}_4F_3(\frac1{16})$
par: Rathie, Arjun K., et autres
Publié: (2023)

Non-symmetric Jacobi polynomials of type $BC_1$ as vector-valued polynomials Part 2: Shift operators
par: van Horssen, Max, et autres
Publié: (2024)

Power series expansion of Wilf function
par: Qi, Feng
Publié: (2021)

On the Fourier transform of regularized Bessel functions on complex numbers and Beyond Endoscopy over number fields
par: Qi, Zhi
Publié: (2018)

Large-degree asymptotic expansions for the Jacobi and related functions
par: Nemes, Gergő
Publié: (2024)

Recurrence relations and applications for the Maclaurin coefficients of squared and cubic hypergeometric functions
par: Mao, Zhong-Xuan, et autres
Publié: (2026)

Series over Bessel functions as series in terms of Riemann's zeta function
par: Tričković, Slobodan B., et autres
Publié: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"e4257bc30115d3e1329f8c8f37de1cec"
ui	"standard"
language	"fr"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790887903.5345 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "e4257bc30115d3e1329f8c8f37de1cec" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"VUFIND_SESSION=e4257bc30115d3e1329f8c8f37de1cec; ui=standard; language=fr"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"12246"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2506_06885/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2506_06885/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790887903.5305
REQUEST_TIME	1790887903

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler